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\(A=\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{36\times37\times38}+\frac{1}{37\times38\times39}\)
\(2A=\frac{2}{1\times2\times3}+\frac{2}{2\times3\times4}+\frac{2}{3\times4\times5}+...+\frac{2}{36\times37\times38}+\frac{2}{37\times38\times39}\)
\(2A=\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+...+\frac{1}{37\times38}-\frac{1}{38\times39}\)
\(2A=\frac{1}{1\times2}-\frac{1}{38\times39}\)
\(2A=\frac{741}{1482}-\frac{1}{1482}\)
\(2A=\frac{370}{741}\)
\(A=\frac{370}{741}:2=\frac{185}{741}\)
Sửa đề chút:
\(\frac{1}{1x2x3}+\frac{1}{2x3x4}+...+\frac{1}{98x99x100}\)
\(=\frac{1}{2}.\left(\frac{2}{1x2x3}+\frac{2}{2x3x4}+...+\frac{2}{98x99x100}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1x2}-\frac{1}{2x3}+\frac{1}{2x3}-\frac{1}{3x4}+...+\frac{1}{98x99}-\frac{1}{99x100}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{99.100}\right)\)
\(=\frac{1}{4}-\frac{1}{99.200}< 1\)
đpcm
A = 2/1x2x3 + 2/2x3x4 + 2/3x4x5 + ... + 2/36x37x38 + 2/37x38x39
A = 1/1x2 - 1/2x3 + 1/2x3 - 1/3x4 + 1/3x4 - 1/4x5 + ...+ 1/36x37 - 1/37x38 + 1/37x38 - 1/38x39
A = 1/2 - 1/38x39
A = 370/741
Tớ ko chắc là đúng đâu
Suy ra 2A=2/1x2x3+2/2x3x4+2/3x4x5+......+2/38x39x40
2A=3-1/1x2x3+4-2/2x3x4+5-3/3x4x5+........+40-38/38x39x40
2A=1/1x2-1/2x3+1/2x3-1/3x4+1/4x5-1/5x6+........+1/38x39-1/39x40
2A=1/2-1/1560
2A=780/1560-1/1560
2A=779/1560
A=779/1560:2
A=779/1560x1/2
A=779/3120
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.......+\frac{1}{38.39.40}\)
\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+.........+\frac{2}{38.39.40}\)
\(2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{40-38}{38.39.40}\)
\(2A=\frac{3}{1.2.3}-\frac{1}{1.2.3}+\frac{4}{2.3.4}-\frac{2}{2.3.4}+\frac{5}{3.4.5}-\frac{3}{3.4.5}+.......+\frac{40}{38.39.40}-\frac{38}{38.39.40}\)
\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+.......+\frac{1}{38.39}-\frac{1}{39.40}\)
\(2A=\frac{1}{1.2}-\frac{1}{39.40}\)
\(2A=\frac{1}{2}-\frac{1}{1560}\)
\(2A=\frac{779}{1560}\)
\(A=\frac{779}{1560}:2\)
\(A=\frac{779}{3120}\)
Ta có :
\(\frac{1}{2009}+\frac{2}{2009}+....+\frac{2008}{2009}\)
\(=\frac{1+2+....+2008}{2009}\)
\(=\frac{2017036}{2009}=1004\)
Ta có ; \(\frac{1}{2009}+\frac{2}{2009}+\frac{3}{2009}+......+\frac{2008}{2009}\)
\(=\frac{1+2+3+......+2008}{2009}\)
\(=\frac{2017036}{2009}=1004\)
Ta có: \(\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}\)
\(\Rightarrow\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+.....+\frac{1}{37}-\frac{1}{38}+\frac{1}{38}-\frac{1}{39}\)
\(=\frac{1}{2.3}-\frac{1}{38.39}=\frac{41}{247}\)